§2.1SpaceLatticeⅠ.Crystalsversusnon-crystals1.ClassificationoffunctionalmaterialsChapterⅡFundamentalsofCrystallography

Lessonthree§2.1SpaceLatticeⅠ.Crystalsv1材料科學(xué)基礎(chǔ)課件22.Classificationofmaterialsbasedonstructure

Regularityinatomarrangement——periodicornot(amorphous)2.Classificationofmaterials3Crystalline:Thematerialsatomsarearranged inaperiodicfashion.Amorphous:Thematerial’satomsdonothave along-rangeorder(0.1～1nm).Singlecrystal:intheformofonecrystal

grainsPolycrystalline:

grainboundariesCrystalline:Thematerialsato4材料科學(xué)基礎(chǔ)課件5材料科學(xué)基礎(chǔ)課件6Ⅱ.Spacelattice1.

Definition:Spacelatticeconsistsofanarrayofregularlyarrangedgeometricalpoints,calledlatticepoints.The(periodic)arrangementofthesepointsdescribestheregularityofthearrangementofatomsincrystals.2.

TwobasicfeaturesoflatticepointsPeriodicity:Arrangedinaperiodicpattern.Identity:Thesurroundingsofeachpointinthelatticeareidentical.Ⅱ.Spacelattice2.Twobasicfe7材料科學(xué)基礎(chǔ)課件8Alatticemaybeone,two,orthreedimensionaltwodimensionsSpacelatticeisapointarraywhichrepresentstheregularityofatomarrangements

(1)(2)(3)

a

bAlatticemaybeone,two,9Threedimensions

EachlatticepointhasidenticalsurroundingenvironmentThreedimensionsEachlattice10Ⅲ.UnitcellandlatticeconstantsUnitcellisthesmallestunitofthelattice.Thewholelatticecanbeobtainedbyinfinitiverepetitionoftheunitcellalongit’sthreeedges.Thespacelatticeischaracterizedbythesizeandshapeoftheunitcell.Ⅲ.Unitcellandlatticeconsta11材料科學(xué)基礎(chǔ)課件12Howtodistinguishthesizeandshapeofthedeferentunitcell?

Thesixvariables,whicharedescribedbylatticeconstants

——

a,b,c;α,β,γHowtodistinguishthesizean13LatticeConstantsa

c

b

αβγa

c

b

αβγLatticeConstantsacbαβγa14§2.2CrystalSystem&LatticeTypes

Ifarotationaroundanaxispassingthroughthecrystalbyanangleof360o/ncanbringthecrystalintocoincidencewithitself,thecrystalissaidtohavean-foldrotationsymmetry.Andaxisissaidtoben-foldrotationaxis.

Weidentify14typesofunitcells,orBravaislattices,groupedinsevencrystalsystems.§2.2CrystalSystem&Lattice15Ⅰ.Sevencrystalsystems

Allpossiblestructurereducetoasmallnumberofbasicunitcellgeometries.Thereareonlyseven,uniqueunitcellshapesthatcanbestackedtogethertofillthree-dimensional.Wemustconsiderhowatomscanbestackedtogetherwithinagivenunitcell.Ⅰ.SevencrystalsystemsAl16SevenCrystalSystemsTriclinica≠b≠c

，α≠β≠γ≠90°Monoclinica≠b≠c

，α＝β＝90°≠γ

α＝γ＝90°≠βOrthorhombica≠b≠c

，α＝β＝γ＝90°Tetragonala＝b≠c

，α＝β＝γ＝90°Cubica＝b＝c

，α＝β＝γ＝90°Hexagonala＝b≠c

，α＝β＝90°γ＝120°Rhombohedrala＝b＝c

，α＝β＝γ≠90°SevenCrystalSystemsTriclinic17Ⅱ.14typesofBravaislattices1.DerivationofBravaislatticesBravaislatticescanbederivedbyaddingpointstothecenterofthebodyand/orexternalfacesanddeletingthoselatticeswhichareidentical.Ⅱ.14typesofBravaislattices187×4＝28Deletethe14typeswhichareidentical28－14＝14+++PICF7×4＝28+++PICF192.14typesofBravaislatticeTricl:simple(P)Monocl:simple(P).base-centered(C)Orthor:simple(P).body-centered(I).base-centered(C).face-centered(F)Tetr:simple(P).body-centered(I)Cubic:simple(P).body-centered(I).face-centered(F)Rhomb:simple(P).Hexagonal:simple(P).2.14typesofBravaislattice20材料科學(xué)基礎(chǔ)課件21Crystalsystems(7)Latticetypes(14)PCFI

ABC1Triclinic√2Monoclinic√√or√(γ≠90°orβ≠

90°

)3Orthorhombic√√or√or√√√4Tetragonal√√5Cubic√√√6Hexagonal√7Rhombohedral√SevencrystalsystemsandfourteenlatticetypesCrystalsystemsLatticetypes(22Ⅲ.PrimitiveCellForprimitivecell,thevolumeisminimumPrimitivecellOnlyincludesonelatticepointⅢ.PrimitiveCellPrimitivecell23Ⅳ.ComplexLatticeTheexampleofcomplexlattice120o120o120oⅣ.ComplexLattice120o120o120o24ExamplesandDiscussions1.Whyarethereonly14spacelattices?

ExplainwhythereisnobasecenteredandfacecenteredtetragonalBravaislattice.ExamplesandDiscussions1.Why25P→CI→FButthevolumeisnotminimum.P→CI→FButthevolumeisno262.CriterionforchoiceofunitcellSymmetryAsmanyrightangleaspossibleThesizeofunitcellshouldbeassmallaspossible2.Criterionforchoiceofuni27Exercise1.Determinethenumberoflatticepointspercellinthecubiccrystalsystems.Ifthereisonlyoneatomlocatedateachlatticepoint,calculatethenumberofatomsperunitcell.2.DeterminetherelationshipbetweentheatomicradiusandthelatticeparameterinSC,BCC,andFCCstructureswhenoneatomislocatedateachlatticepoint.3.DeterminethedensityofBCCiron,whichhasalatticeparameterof0.2866nm.Exercise1.Determinethenumbe284.ProvethattheA-face-centeredhexagonallatticeisnotanewtypeoflatticeinadditiontothe14spacelattices.5.DrawaprimitivecellforBCClattice.Thankyou!34.ProvethattheA-face-cente29§2.1SpaceLatticeⅠ.Crystalsversusnon-crystals1.ClassificationoffunctionalmaterialsChapterⅡFundamentalsofCrystallography

Lessonthree§2.1SpaceLatticeⅠ.Crystalsv30材料科學(xué)基礎(chǔ)課件312.Classificationofmaterialsbasedonstructure

Regularityinatomarrangement——periodicornot(amorphous)2.Classificationofmaterials32Crystalline:Thematerialsatomsarearranged inaperiodicfashion.Amorphous:Thematerial’satomsdonothave along-rangeorder(0.1～1nm).Singlecrystal:intheformofonecrystal

grainsPolycrystalline:

grainboundariesCrystalline:Thematerialsato33材料科學(xué)基礎(chǔ)課件34材料科學(xué)基礎(chǔ)課件35Ⅱ.Spacelattice1.

Definition:Spacelatticeconsistsofanarrayofregularlyarrangedgeometricalpoints,calledlatticepoints.The(periodic)arrangementofthesepointsdescribestheregularityofthearrangementofatomsincrystals.2.

TwobasicfeaturesoflatticepointsPeriodicity:Arrangedinaperiodicpattern.Identity:Thesurroundingsofeachpointinthelatticeareidentical.Ⅱ.Spacelattice2.Twobasicfe36材料科學(xué)基礎(chǔ)課件37Alatticemaybeone,two,orthreedimensionaltwodimensionsSpacelatticeisapointarraywhichrepresentstheregularityofatomarrangements

(1)(2)(3)

a

bAlatticemaybeone,two,38Threedimensions

EachlatticepointhasidenticalsurroundingenvironmentThreedimensionsEachlattice39Ⅲ.UnitcellandlatticeconstantsUnitcellisthesmallestunitofthelattice.Thewholelatticecanbeobtainedbyinfinitiverepetitionoftheunitcellalongit’sthreeedges.Thespacelatticeischaracterizedbythesizeandshapeoftheunitcell.Ⅲ.Unitcellandlatticeconsta40材料科學(xué)基礎(chǔ)課件41Howtodistinguishthesizeandshapeofthedeferentunitcell?

Thesixvariables,whicharedescribedbylatticeconstants

——

a,b,c;α,β,γHowtodistinguishthesizean42LatticeConstantsa

c

b

αβγa

c

b

αβγLatticeConstantsacbαβγa43§2.2CrystalSystem&LatticeTypes

Ifarotationaroundanaxispassingthroughthecrystalbyanangleof360o/ncanbringthecrystalintocoincidencewithitself,thecrystalissaidtohavean-foldrotationsymmetry.Andaxisissaidtoben-foldrotationaxis.

Weidentify14typesofunitcells,orBravaislattices,groupedinsevencrystalsystems.§2.2CrystalSystem&Lattice44Ⅰ.Sevencrystalsystems

Allpossiblestructurereducetoasmallnumberofbasicunitcellgeometries.Thereareonlyseven,uniqueunitcellshapesthatcanbestackedtogethertofillthree-dimensional.Wemustconsiderhowatomscanbestackedtogetherwithinagivenunitcell.Ⅰ.SevencrystalsystemsAl45SevenCrystalSystemsTriclinica≠b≠c

，α≠β≠γ≠90°Monoclinica≠b≠c

，α＝β＝90°≠γ

α＝γ＝90°≠βOrthorhombica≠b≠c

，α＝β＝γ＝90°Tetragonala＝b≠c

，α＝β＝γ＝90°Cubica＝b＝c

，α＝β＝γ＝90°Hexagonala＝b≠c

，α＝β＝90°γ＝120°Rhombohedrala＝b＝c

，α＝β＝γ≠90°SevenCrystalSystemsTriclinic46Ⅱ.14typesofBravaislattices1.DerivationofBravaislatticesBravaislatticescanbederivedbyaddingpointstothecenterofthebodyand/orexternalfacesanddeletingthoselatticeswhichareidentical.Ⅱ.14typesofBravaislattices477×4＝28Deletethe14typeswhichareidentical28－14＝14+++PICF7×4＝28+++PICF482.14typesofBravaislatticeTricl:simple(P)Monocl:simple(P).base-centered(C)Orthor:simple(P).body-centered(I).base-centered(C).face-centered(F)Tetr:simple(P).body-centered(I)Cubic:simple(P).body-centered(I).face-centered(F)Rhomb:simple(P).Hexagonal:simple(P).2.14typesofBravaislattice49材料科學(xué)基礎(chǔ)課件50Crystalsystems(7)Latticetypes(14)PCFI

ABC1Triclinic√2Monoclinic√√or√(γ≠90°orβ≠

90°

)3Orthorhombic√√or√or√√√4Tetragonal√√5Cubic√√√6Hexagonal√7Rhombohedral√SevencrystalsystemsandfourteenlatticetypesCrystalsystemsLatticetypes(51Ⅲ.PrimitiveCellForprimitivecell,thevolumeisminimumPrimitivecellOnlyincludesonelatticepointⅢ.PrimitiveCellPrimitivecell52Ⅳ.ComplexLatticeTheexampleofcomplexlattice120o120o